Anyone who sees "The Suicide Squad" in the cinema will notice that the film follows the continuity of its predecessor. Not only has James Gunn retained four of the actors and their respective roles, but these four characters have a clear relationship to one another in the film. In particular, a kind of friendship is shown between Harley Quinn (Robbie) and Rick Flag (Kinnaman), in dialogues it is even mentioned that the two have a common history that they do not share with the other characters. That backstory is - of course - "Suicide Squad".
At the beginning of the film, Captain Boomerang (Courtney) even asks his girlfriend Harley why she is part of the "Suicide Squad" again. Not only does this mention that this Suicide Squad has been around for a long time, it also alludes to the fact that Harley Quinn escaped from prison at the end of the 2016 film and then went on a solo adventure in the film Harley Quinn: Birds of Prey experienced freedom.
But you don't have to have seen "Suicide Squad" or "Harley Quinn: Birds of Prey" to enjoy the new "The Suicide Squad" in the cinema: Apart from these few allusions, the plot of the new film stands completely for itself. James Gunn did his own thing - but at least he didn't deny the previous films.
A small tip, however: If you have absolutely no idea what exactly the principle behind the Suicide Squad is all about, you should at least read a summary of the first film. Gunn doesn't explain that much again, whereas the original film spent almost half of its run time explaining the concept of "Suicide Squad".